1) Consider a health insurance market in Gollumania with each customer having an expected health care cost for the next year. This expected health care cost is distributed uniformly between 0 and $40,000. In health insurance market there is one neutral insurance company offering full coverage with a premium of $P. Customers are identical in their preferences and they are risk neutral. They buy the insurance if . Insurers cant detect whether individuals are sick or healthy. So, individuals expected health care costs for the next year is private information.

a) On a graph show distribution of expected health care costs for the next year.

b) Given a premium level of $20,000 which individuals buy the insurance?

c) What is the expected health care cost of the insured if health insurance premium is $20,000?

d) Calculate the insurance firms profit.

e) Assume the health insurance firm increases premium level to $30,000. Repeat a) d). Is the health insurance market stable?

f) Now consider the case if individuals are risk averse and value being insured more than their expected costs. Now they buy the insurance if . Moreover Governor Gollu started a health insurance program, GolluCare that covers individuals in the highest risk group. Based on age, pre-existing conditions and other risk factors individuals with more than $30,000 of expected health care costs are covered under GolluCare. Find a premium level that keeps the insurance company with zero profit. Is the market stable?